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Mysteries of Geometric Optics In MTW Chapter 22
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[QUOTE="TSny, post: 6494693, member: 229090"] The introduction of the parameter ##\varepsilon## is just a convenient way to "tag" the various terms so that the power of ##\varepsilon## immediately tells you the order of the term in [S]λ[/S]/L. A term with ##\varepsilon^2## is second order in [S]λ[/S]/L even when ##\varepsilon = 1##. If you want, you could forgo introducing ##\varepsilon##. But, then, you would need to remember that ##a^\mu## is zero order in [S]λ[/S]/L, ##b^\mu## is first order, ##c^\mu## is second order, ##\theta## is order -1,etc. When MTW "collect terms of order ##\epsilon^n##", they are just collecting terms of order ([S]λ[/S]/L)[SUP]n[/SUP], which you could do even if you didn't introduce ##\varepsilon##. [/QUOTE]
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Mysteries of Geometric Optics In MTW Chapter 22
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